5. D. Hamann CSIRODivision of Applied Chemistry Box 4331, G.P.O.
Melbourne, Australia
Titration Behavior of Monoprotic and Diprotic Acids
Sturrockl has pointed out in THrs that it is often possible to distinguish between a weak diprotic acid and a weak monoprotic one by measuring the change of pH between the 25% and 75% neutralization points. He concluded that, except in very dilute solutions, this change ApH is equal to loglo9 = 0.9542 for a monoprotic acid, but is considerably greater for a diprotic acid. JOURNAL
The purpose of the present note is to define the conditions of concentration and of pK for which Sturrock's criterion is valid and to give theoretical and experimental examples of its limitations. Values of ApH that are exact except for activity coefficient corrections can be calculated from the equation~~,~
STURROCK, P. E., J. CHEM.EDUC., 45, 2.59 (1968). See, for instance, FLECK, G. M., "Equilibria. in Solution," Holt, Rinehart, and Winston, Inc., New Yark, 1966, p. 84. The author has compiled a program to solve these equations on the Hewlett-Paekard 9100A desk calculator. Copies of the propram are available on request.
Figure 1. Theoretical vmluer of ApH for monoprotic mid. Isolid line) with ionirotion constants Kt, and diprotic acids (broken line) with ionirotion constants KI and Kz = K1/SO. The number on each curve denotes the molarity e. of tho acid.
658 / Journal o f Chemicol Educofion
Figure 2. Experimental and theoretical curves for the litralion of 1.0 M monochlorpocetic ocid (solid line) ond 0.01 M rac-2.3-dibmmosuccinic ocid (broken line). The curves A are bored on exact cdculotionr and B on opproximote calculdionr (see text). a denotes the degree of neutrdiralion.
IH+l4
+ [H+Ia(b+ K , ) + lH+12(bK,- aK, + KIK* -Ku) + [H+lK,(bK1- 2aK1 - K,)
+ vd w d ( v a + us)
- K,K&
=
0
(1)
a = v,c./(u,
(2)
b =
(3)
where, for a dipmtic acid, Kl and K p are the first and second ionization constants and for a monoprotic acid Kl is the ionization constant and K2 = 0. Kmdenotes the ionization constant of water; [ H + ]is the hydrogen ion concentration; c. and ca are the concentrations of the separate acid and base solutions; .u and vo are the volumes of each that have been put into the mixture, and a and b are the corresponding numbers of moles per liter of acid and base in the mixture. To obtain results of any generality it is necessary to assume that dilution effects are unimportant, that is, that ca >> c., v*
